Question

Rút gọn a) M= 2¹⁰⁰ -  2⁹⁹ + 2⁹⁸ - 2⁹⁷ +.....+ 2² - 2

b) N= 3¹⁰⁰ - 3⁹⁹ + 3⁹⁸ - 3⁹⁷ +.....+ 3² - 3 + 1

Answer 1

M = \(2^{100-}2^{99}+2^{98}-...+2^2-2\)

\(2M=2^{101}-2^{100}+2^{99}-2^{98}+2^{97}+...+2^3-2^2\)

\(2M+M=2^{101}-2\)

\(M=\frac{2^{101}-2}{3}\)

Answer 2

N=\(3^{100}-3^{^{ }99}+3^{98}-3^{97}+...+3^2-3+1\)

\(3N=3^{101}-3^{100}+3^{99}-3^{98}+3^{97}+...+3^3-3^2+3\)

3N+N= 4N = \(3^{101}+1\)

N=\(\frac{3^{101}+1}{4}\)